Backward waveguide having a dielectric contiguous with one inner wall thereof



BACKWARD WAVEGUIDE HAVING A DIELECTRIC CONTIGUOUS WITH ONE INNER WALL THEREOF" 4 Sheets-Sheet 1 Nov. 7, 1967 H. G. UNGER ETAL 3,351,877

Filed July 20.- 1964 Fig. I

Fig.2 PRIOR ART INVEN ToRs Hons Georg Unger 8| Arne Lovik awWj ATTORNEYS 1967 H. e. UNGER ETAL 77 BACKWARD WAVEGUIDE HAVING A DIELECTRIC CONTIGUOUS WITH ONE INNER WALL THEREOF Filed July 20. 1964 4 Sheets-Sheet 2 Fig. 4

INVENTORS Horis Georg Unger 8 Arne Lovik BYM/ ATTO RNE Y8 Nov. 7, 1967 H. G. UNGER ETAL 3,351,877

' BACKWARD WAVEGUIDE HAVING' A DIELECTRIC CQNTIGUOUS WITH ONE INNER WALL THEREOF Filed July 20. 1964 4 Sheets-Sheet 5 Q Fig. 6

Fig.0 Fig. 7 10b m I 4: Y [g d 4* 1 1 /11 I INVEN'TORS Hons Georg Unger8\ Arne Luvik [WW e 7%:

ATTORNE Y5 Nov. 7, 1967 H. G. UNGER ETAL 3,351,877

' BACKWARD WAVEGUIDE HAVING A DIELECTRIC CONTIGUOUS WITH ONE INNER WALL THEREOF Filed July 20. 1964 4 Sheets-Sheet 4 FIG.9.

INVENTORS F|G |3 Hons Georg Un'geir 8 Arne Lavik BY Maw/" ATTORNEYS United States Patent ()fifice 3,351,877 Patented Nov. 7, 1967 3,351,877 BACKWARI) WAVEGUIDE HAVING A DIELEC- TRIC CGNTIGUGUS WITH ONE INNER WALL THEREOF Hans Georg Unger and Arne Lavik, Braunschweig,

Germany, assignors to Telefunken Patentverwertungs-G.m.b.H., Ulm (Danube), Germany Filed July 20, 1964, Ser. No. 383,757 Claims priority, application Germany, July 20, 1963, T 24,338 3 Claims. (Cl. 333-98) ABSTRACT OF THE DISCLOSURE A waveguide for backward waves, i.e., electromagnetic waves whose group velocity has a direction opposite to that of its phase velocity, is formed by appropriately dimensioning a waveguide and a dielectric within the wave guide. The dielectric is in the form of an elongated strip which is smaller in cross-section than the interior of the waveguide and which extends in the direction of propagation of the waveguide contiguous with one inner wall thereof.

The present invention relates to wave guides and, more particularly, to an arrangement for backward waves, comprising a hollow wave guide section with a dielectric extending in the propagation direction of the waves and only partially filling the wave guide cross section.

It has been known that, in wave guides which are periodically under load, electromagnetic waves can exist whose velocity of propagation is smaller than the propagation velocity of light in free space. Such arrangements are used in traveling wave amplifiers.

Furthermore, it is already known that backward waves exist in a circular wave guide which is provided with a continuously extending, axial dielectric insert. Backward waves are understood to be electromagnetic waves whose group velocity has a direction opposite to that of the phase velocity. In such waves, the energy travels oppositely to the propagation direction of the phase fronts.

To produce a wave guide capable of transmitting backward waves, it would be advantageous if the dielectric insert could be mounted directly in the wave guide wall. However, it has been pointed out in an article by Claricoats, Circular-waveguide backward-wave structures, Proceedings IEE, Feb. 1963, pp. 267, 268, that backward waves can exist in a wave guide only if the dielectric component is axially arranged; if the dielectric component is mounted on a wave guide wall, no backward waves are possible.

It is an object of the present invention to create an arrangement for backward waves which comprises a wave guide section provided with a dielectric extending in the propagation direction of the waves and only partially filling the cross section of the wave guide, in which arrangement a simple mechanical mounting of the required dielectric load is possible. In accordance with the invention, it is proposed for this purpose to fashion the dielectric approximately in the form of a strip, and to have it rest on a wave guide wall.

Through extensive calculations which were experimentally verified, it was discovered, surprisingly, that given certain dimensioning, backward waves can exist in a wave guide in which the dielectric insert rests directly upon the wave guide wall. In place of a single strip of dielectric material, several strips may be used, all of which are mounted on a single wall of the wave guide.

Additional objects and advantages of the present invention will become apparent upon consideration of the 01- lowing description when taken in conjunction with the accompanying drawings in which:

FIGURE 1 is a plot of the phase characteristics of a backward wave, in which frequency on the vertical axis is plotted against the phase constant on the horizontal axis.

FIGURE 2 is a cross-sectional view of a circular wave guide known in the prior art.

FIGURE 3 is a cross section of an embodiment of a wave guide according to the present invention.

FIGURE 4 is a plot of various phase characteristics of the wave guide section of FIGURE 3, wherein frequency is plotted on the vertical axis against phase constant on the horizontal axis.

FIGURE 5 is a cross-sectional view of a wave guide according to a different embodiment of the invention.

FIGURE 6 is a plot of various phase characteristics of the arrangement of FIGURE 5.

FIGURE 7 is a graph of the relative frequency range of an embodiment of the invention plotted against the ratio of the air gap width to the wave guide breadth.

FIGURE 8 illustrates a further embodiment of the invention utilizing a wave guide of U-shaped cross section.

FIGURE 9 shows in cross section, a wave guide according to the invention wherein several dielectric strips are mounted on a common wall.

FIGURE 10 is a perspective View of a wave guide having a tapered dielectric.

FIGURE 11 shows a cross section of a contra-direction coupler.

FIGURE 11a is a sectional view taken on line 11a--11a of FIGURE 11.

FIGURE 12 is a perspective view of a leakage wave antenna.

FIGURE 13 shows in cross section a wave guide according to the invention with one dielectric strip mounted on the bottom of the guide.

With more particular reference to the drawings, FIG- URE 1 shows the phase characteristics of a backward wave. This curve has a descending branch between the two points e and b. At each frequency in this region, two natural waves can propagate in the wave guide. One of these waves is the backward wave. Its phase constants are designated 51 and 8 in FIGURE 1. The wave lengths pertaining thereto are designated a, and In FIGURE 1, the phase constant B was plotted in dependence upon the frequency f. The frequency at point b is the inversion frequency f,,. The cutofi? frequency is designated f In FIGURE 2, a circular wave guide 1 is illustrated in cross section. This wave guide has an axial insert 2 of dielectric material. In this arrangement, calculation and experimentation showed backward waves to exist. However, in practical applications dealing with backward *waves, the use of a circular wave guide is disadvantageous because the backward waves forming therein do not have an unequivocally defined polarization direction. In addition, there is the disadvantage that the dielectric insert 2 must be mounted within the wave of the dielectric strip 5 is designated with r in the figure,

while the radius of the semi-circular wave guide is r,,. In FIGURE 4, various phase characteristics I to IV of the wave guide section illustrated in FIGURE 3 are plotted in dependence upon the frequency f. The upper 3 phase curve designated with I was plotted at a relationship of n /r ==0.5. In case of the curve designated with II, this relationship amounted to 0.6, in the third curve [III] 0.7, and in case of the lowermost phase curve [IV] 0.8. The relative dielectric constant (that is, the ratio of the dielectric constant of the dielectric strip to that of the medium between the strip and the wave guide) must, in an arrangement constructed according to FIG- URE 3, be greater than 9.1 in order to obtain backward waves. In the four phase curves illustrated in FIGURE 4, the relative dielectric constant of the insert was 15. In order to be able to better judge the course of the curves, two auxiliary lines are additionally drawn into the plot of FIGURE 4. The solid line corresponds to a phase velocity The dashed line designates the phase velocity which is equal to the speed of light c. The relative frequency range which can be utilized, in which a backward wave occurs in an arrangement constructed in accordance with FIG- URE 3, amounts to 9.5%. The relative frequency range may be defined as (j In FIGURE 5, a further embodiment of the invention is illustrated. Here, the wave guide section is a rectangle 6 which is loaded on its longer side a with a dielectric strip 7. The height of the dielectric strip 7, which is arranged symmetrically on side a, is designated h, and its breadth t.

FIGURE 6 shows five phase characteristics of the arrangement shown in FIGURE 5 with various dimensional relationships. Instead of the calibration curves of FIGURE 4, here the phase curves were plotted in a normalized manner. On the horizontal axis, the phase constant ,6 is plotted, multiplied by the wave guide breadth a; the unit of the vertical axis is the product of the angular frequency w and the wave guide breadth a, divided by the velocity of light 0. As in FIGURE 4, two auxiliary straight lines are shown in FIGURE 6, which indicates special values of the phase velocity v The curves I to V again show the path of the phase of the fundamental wave in the wave guide section. With the arrangement illustrated in FIGURE 5, backward waves are obtained if the relative dielectric constant of the strip 7 is larger than 8.5. In order to determine the optimal dispersion characteristic, i.e., the phase characteristics with a descending branch over as broad a frequency range as possible, all parameters were systematically varied. An optimum was obtained at a relative dielectric constant of the dielectric strip 7 of 15, with a geometrical relationship of The relative frequency range was 11.7%. In the case of the phase curves illustrated in FIGURE 6, the height h of the dielectric was half the length of the longer side of the wave guide, the air gap 0. above the dielectric was varied. The curve designated with I represents the phase characteristic of an arrangement in which d=0.18a. In the case of the phase curve II, d was 0.4a. The curve designated III represents the condition in which the air gap d was exactly as large as the wave guide breadth a. In curves IV and V the air gaps were 0.1a and 0.01a, respectively.

In FIGURE 7, the relative frequency range Af/f is plotted as a function of the ratio of air gap a to wave guide breadth a. Af here designates the difference between limiting frequency I and inversion frequency f For very large values of d/a, the relative frequency range of the backward wave asymptotically approaches a constant value. From this behavior, it can be seen that even in a U-shaped wave guide, backward waves exist. This can be explained by the fact that, for correspondingly high values of d/a, the fields of the backward waves have nearly vanished at the upper wall of the wave guides, so that this wall can be removed without substantially interfering with the backward waves.

FIGURE 8 shows as a further embodiment of the invention a wave guide of U-shaped cross section. On the shorter side 9 of this U-shaped wave guide, is a dielectric strip 8. In the example illustrated, this strip is arranged symmetrically with respect to the two side walls 10a and 10b of the wave guide. The height of the dielectric strip 8 is designated h in this figure, and the breadth is designated t. The height of each side wall of the wave guide is [h-l-d]. The relative dielectric constant of strip 8 must be chosen to be larger than 4.8 in order to create backward waves.

It is self-evident that the cross sections of the dielectric strips illustrated in the embodiments represent only a few of the many possible embodiments of the invention.

If the dielectric strip of the wave guide section is formed at least in parts by a material having a dielectric constant or a permeability constant dependent upon the strength of the field surrounding it, numerous applications are possible. For example, the relative dielectric or permeability constant may be set by means of an external static field, so that either forward or backward waves may be selected to occur in the wave guide section.

It is also possible to use a wave guide section constructed in accordance with the invention as a transit time member, or delay line, to compensate another network. In this case, the arrangement is designated such that phase curves are obtained in the frequency range of interest which are complementary to the phase curves of the fourpole (or four terminal device) to be compensated. If the output terminals of the four-pole device are made up of a wave guide, a wave guide section according to the invention with a dielectric designed as described above, is inserted in the wave guide system, for the purpose of compensation. If this is done, undesirable discontinuities may occur in the phase curve of the system, since at those points where the wave guide sections are joined the cross section of the dielectric strip may change abruptly. In order to avoid these discontinuities, it is recommended that the dielectric strip be made to taper off at its ends in a manner known per se, as is illustrated in FIGURE 10.

A further possibility of application of the inventive arrangement is in the art of direction couplers. Here, a rectangular wave guide is coupled with a wave guide section equipped with a dielectric according to the invention, coupling being accomplished via corresponding coupling openings in the side wall of the rectangular wave guide. As one of the wave guides conducts forward waves, and the other backward waves, energy is not coupled from one wave to the other in the same propagation direction, but in the opposite direction, and at the same phase velocity, but at opposite group velocity of the two coupled waves. Such direction couplers are therefore called contra-direction couplers.

FIGURES 11 and 11a show an embodiment of a contro-direction coupler which is according to the invention designed to operate at the frequency of 8 gc./s. FIG- URES 11 and 11a are drawn to the scale 1:2. The dielectric strip is made from stycast of relative dielectric constant 15. Wave guide 11 is according to the invention loaded with a dielectric strip 12 to propagate a backward wave which is matched at the frequency of operation in phase constant to the phase constant of the fundamental mode of propagation in wave guide 13. Wave guide 12 and wave guide 13 are electrically connected by an array 14 of holes or slots in a common wall.

The inventive construction of a wave guide section also makes it possible to build radiation arrangements of the surface wave or leakage wave antenna type. For this purpose, a wave guide section which can transmit backward waves is provided with suitable openings for radiating electromagnetic waves.

FIGURE 12 illustrates an embodiment of a leakage wave antenna radiating according to the invention from a backward wave. Wave guide section 16 is of standard size for the specific operating frequency. Tapered transition 17 is one to three free space wave lengths long. Trough guide 18 is loaded with a square dielectric strip 19 of relative dielectric constant 6 and with half the width of the trough guide.

The following description of a specific example of a wave guide constructed according to the invention is given by way of example and is not intended to limit the scope of the invention in any way. With reference to FIGURE 13 wave guide 20 is 1.016 cm. wide and 0.6 cm. high. It is loaded with a dielectric strip 21 of stycast with a relative dielectric constant 15, at the center of the bottom wall of wave guide 20. The strip is 0.4 cm. high and 5 cm. wide. The cutofl frequency for the fundamental mode of propagation is 8.6 gc./s. and its inversion frequency 7.7 gc./s. In the frequency range 7.7 to 8.6 gc./s. the fundamental mode of propagation is a backward wave. Its phase constant at the inversion frequency is 1.9 cm.- At an operating frequency of 8 gc./s. the backward wave has a phase constant of 0.8 crnf It will be understood that the above description of the present invention is susceptible to various modifications, changes, and adaptations, and the same are intended to be comprehended within the meaning and range of equivalents of the appended claims.

What is claimed is:

1. A waveguide for conducting backward waves, comprising, in combination: a waveguide, and a dielectric element in the form of an elongated strip within the waveguide and of smaller cross section than the waveguide, the eross section of the waveguide and the cross section of the dielectric element both being semicircular in shape, the fiat side of the dielectric element cross section being contiguous with the flat side of the waveguide cross section, the dielectric element extending in the propagation direction of the waveguide and being symmetrical with respect to the waveguide, the relative dielectric constant of the dielectric element being greater than 9.1, the ratio between the radius of the dielectric element and the radius of the waveguide being between 0.5 and 0.8 inelusive, and the waveguide and dielectric element being so dimensioned as to produce backward waves within said waveguide.

2. A waveguide for conducting backward waves, comprising, in combination: a waveguide, and a dielectric element in the form of an elongated strip within the waveguide and of smaller cross section than the waveguide, contiguous with one wall thereof and extending in the propagation direction thereof, the cross section of the waveguide being rectangular in shape and the dielectric element being symmetrical and contiguous with one of the longer sides of the rectangular cross section of the Waveguide, the relative dielectric constant of the dielectric element being greater than 8.5, the dielectric element being rectangular in cross-sectional shape and having the dimensions t-h where t is the dimension parallel to the longer dimension of the waveguide and h is the dimension at right angles to t, the waveguide having the cross-sectional dimensions a- (h+d), where a is the longer dimension of the waveguide and a is the gap between the dielectric element and the non-continguous longer side of the waveguide, and wherein the ratio .a:t:h:d is approximately equal to 1:0.5:O.4:0.2.

3. A waveguide as defined in claim 2 wherein the relative dielectric constant of said dielectric element is equal to approximately 15.

References Cited UNITED STATES PATENTS 2,433,368 12/1947 Johnson et a1 333-- X 2,795,698 6/1957 Cutler 333-95 X 2,879,484 3/1959 Miller 33310 X 2,939,092 5/1960 Cook 333--31 X 3,018,480 1/1962 Thourel 343783 X FOREIGN PATENTS 760,388 10/ 1956 Great Britain.

OTHER REFERENCES Sperry Gyroscope Co.: Microwave Transmission, Design Data, Publication No. 23-80. Declassified 1958, pp. 177-178.

HERMAN KARL SAALBACH, Primary Examiner. ELI LIEBERMAN, Examiner.

R. D. COHN, P. L. GENSLER, Assistant Examiner. 

1. A WAVEGUIDE FOR CONDUCTING BACKWARD WAVES, COMPRISING, IN COMBINATION: A WAGEGUIDE, AND A DIELECTRIC ELEMENT IN THE FORM OF AN ELONGATED STRIP WITHIN THE WAVEGUIDE AND OF SMALLER CROSS SECTION THAT THE WAVEGUIDE, THE CROSS SECTION OF THE WAVEGUIDE AND THE CROSS SECTION OF THE DIELECTRIC ELEMENT BOTH BEING SEMICIRCULAR IN SHAPE, THE FLAT SIDE OF THE DIELECTRIC ELEMENT CROSS SECTION BEING CONTIGUOUS WITH THE FLAT SIDE OF THE WAVEGUIDE CROSS SECTION, THE DIELECTRIC ELEMENT EXTENDING IN THE PROPAGATION DIRECTION OF THE WAGEGUIDE AND BEING SYMMETRICAL WITH RESPECT TO THE WAVEGUIDE, THE RELATIVE DIELECTRIC CONSTANT OF THE DIELECTRIC ELEMENT BEING GREATER THAN 9.1, THE RATIO BETWEEN THE RADIUS OF THE DIELECTRIC ELEMENT AND THE RADIUS OF THE WAVEGUIDE BEING BETWEEN 0.5 AND 0.8 INCLUSIVE, AND THE WAVEGUIDE AND DIELECTRIC ELEMENT BEING SO DIMENSIONED AT TO PRODUCE BACKWARD WAVES WITHIN SAID WAVEGUIDE. 